Robot Modeling and Control [Book Review]
(2006)

The field of robotics began in the 1960s and 1970s with the design and control of general purpose robotic manipulators. During the 1980s the expense of integrating robotics into manufacturing lines and the difficulty of performing seemingly easy tasks, such as manipulating flexible objects or washing a window, led to disenchantment among many researchers and funding agencies. Since the 1990s the popularity of robotics has resurged with many new exciting areas of application particularly in the medical, defense, and service sectors. Robotics has grown from a field that is primarily concerned with problems such as the manipulation of rigid bodies in well-structured environments to a field that has tackled challenging problems such as extraterrestrial exploration and remote minimally invasive surgery. I began my involvement in the field of robotics as a graduate student studying control theory. My project was to design a control algorithm to induce stable walking in a biped robot. As with many control problems, before formulating a solution I had to determine a suitable model for the plant. Since I was an electrical engineering student with little background in the kinematics and dynamics of rigid-body mechanical systems, this task was daunting. With some guidance from a fellow student, I fumbled my way through Lagrange’s method to derive the robot’s equations of motion. I had little idea at the time why forming the Lagrangian and taking certain derivatives resulted in the right equations. For insight I was pointed to various texts on classical mechanics. While these texts provided the desired insight, I was still left with questions: Given an arbitrary system, how do I systematically construct the Lagrangian so that I can derive the system’s equation of motion? What are the most effective techniques for robot control? What special aspects of the robot’s dynamics should be considered in developing controllers? Five years after my introduction to the field of robotics, I now know that research in the field goes well beyond the dynamics and control of traditional manipulators. The concepts required to analyze and control manipulators, however, are still needed in modern robotics research. These fundamental concepts, which are addressed by many introductory texts on robotics, are the following: 1) Forward kinematics: Given joint displacements, determine the position and orientation of the endeffector with respect to a specified reference frame. 2) Inverse kinematics: Given the position and orientation of the end-effector frame relative to a specified reference frame, determine the joint variables that give rise to this configuration. 3) Differential kinematics: Given the manipulator’s joint rates, determine the linear and angular velocities of the end-effector frame relative to a fixed reference frame. 4) Statics: Given the forces and moments applied to the manipulator, determine the corresponding joint forces and torques required to maintain equilibrium in the presence of applied forces and moments. 5) Dynamics: Determine the equations of motion of the system. Specifically, determine the differential equations relating the applied forces and torques to the joint variables, joint rates, and joint accelerations. 6) Trajectory generation: Given initial and final configurations of the manipulator, find a trajectory of the joint variables connecting these two configurations. 7) Control: Given desired joint trajectories or forces between the end-effector and the environment determine joint torques and forces that effect these joint trajectories and forces.